Abstract: We propose a new approximate factorization for solving linear systems with
symmetric positive definite sparse matrices. In a nutshell the algorithm is to
apply hierarchically block Gaussian elimination and additionally compress the
fill-in. The systems that have efficient compression of the fill-in mostly
arise from discretization of partial differential equations. We show that the
resulting factorization can be used as an efficient preconditioner and compare
the proposed approach with state-of-art direct and iterative solvers.